IB Math IA: Volume of a Revolution
Access all videos at mrflynnib.com.
In this video we use Geogebra to create a solid of revolution. Volume of a revolution is a solid (excuse the pun) idea for the IB Math IA.
Access all videos at mrflynnib.com.
In this video we use Geogebra to create a solid of revolution. Volume of a revolution is a solid (excuse the pun) idea for the IB Math IA.
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Lessons on every topic, all IA videos and full past paper solutions at mrflynnib.com.
This is incredible, thank you as a maths teacher!
Very concise and clear. Thank you Mr Flynn
@MrFlynnIB
8 ай бұрын
@neilmurfin7775 Thanks Mr. Murf I learnt from the best.
"you have weeeks and months to do your ia" me:doing it 5 hours before summissiong euiaseghfksag
@cyover4401
5 ай бұрын
literally me rn istfg
@chizyberry5205
4 ай бұрын
@@cyover4401 fr, mine is due in 2 days lol
Excellent Video Again thank you
Nice man ur genius love u
How would I find the surface area and volume of a solid of no revolution? and how would I optimize it? I can't find a good explanation online
Hello, my math teacher told me to go in the direction of looking at how the shell and disc methods were derived and to analyse their strengths and weaknesses in finding the volume of various solids that have different parameters. However, after alot of research im unable to find anything substantial to talk about in terms of strengths and weaknesses as it is very shallow. Do you have any advice regarding this?
Hello! Do you think the topic of determining if russian dolls's volume decrease arithmetically or geometrically work? I will look at calc and sequences but I'm not so sure on the sequences part.
@MrFlynnIB
2 жыл бұрын
I love it.
Hi, sir. Loving the videos! Do you have any suggestions of how I could use calculus in my Maths AA HL IA (possible involving volume of revolution) and relate it with medicine/biology? All the ideas I previously had were rejected since they weren't viable...
@MrFlynnIB
2 жыл бұрын
Ya a volume of revolution IA involving some medical product. Maybe a tablet or something 3d printed. You'll have to find something. I have also had in the past a very good IA modelling the ECG of a healthy heart and an unhealthy heart. He then looked at the area under the curves and compared. There is lots of data out there that you can use to create a model. Like number of covid cases or hospitalisations, etc. Hope that helps.
Hey sorry for asking so many questions, my teacher is unavailable for the week (The IA is due next week). I'm considering using the Lagrange quadratic interpolation formula to find three functions for three parts of a beauty blender and reflect it to obtain a relation modeling the beauty blender and using it to calculate the volume and surface area. Could I use the polynomial given by GeoGebra to validate the calculated volume and surface area?
@MrFlynnIB
Жыл бұрын
You can do all that and it sounds good but the important part is to show your understanding throughout the IA. Don't do anything you don't fully understand.
Nice explanation and great idea. One question tho: how do I measure the volume now? Do I put the equation g(x) in the volume of revolution formula? If so, what are the limits? is it from 0 to highest distance in the x-axis or y-axis? Thank you for everything.
@MrFlynnIB
2 жыл бұрын
Ya exactly.
Hey, Mr. Flynn! Great video, really appreciate it. I am thinking of modeling and finding the volume of a symmetrical sports bottle I have. I am also thinking of finding a way to find the volume in real life and compare the two to help build a complexity in my IA. Does this sound like a good plan?
@MrFlynnIB
5 ай бұрын
Yes it does.
Hi! This is very helpful sir. I have a recent IA due for math SL (just started). I was wondering that is it possible to do the calculations by hand? And then compare them with the technology one?. Also I was considering if I can submerge my coke bottle(the object I am using) into water and compare the 2 volumes. My teacher said the water part was a bit too much. I don't know now. And since we haven't learnt this concept formally in class, I am on my own. Is there a good resources where I can learn from(that includes everything I need to know). Thank you so much!
@MrFlynnIB
Жыл бұрын
Yes. Sounds good. The water idea sounds fine to me but remember your teacher is marking it so listen to their advice. I have a video on volume of revolution on my website but I'm sure there are plenty KZread videos too that explain how to do it.
This is awesome! I just wanted to ask, if you have a sample of an IA with this topic?
@MrFlynnIB
2 жыл бұрын
I have samples including this topic on my website. Behind the paywall sorry.
Hi Mr Flynn, thank you for the video! I have a question: is this topic complicated enough to be HL and achieve 7? Also I've learnt Lagrange Multipliers on my own for the IA, but can't find any suitable topic to apply it (they are either too hard or too easy). Do you know any topic which I could apply Lagrange multiplier on?
@MrFlynnIB
Жыл бұрын
Yes to the first question. And sorry, I am not familiar enough with Lagrange multipliers to advise you.
Thanks for this, would you have any building recommendations for me to calculate its volume. I have thought about the burj khalifa but way too overcomplicated, the example I GOT BUT i can't use is the temple of heaven. Would you have any suggestions please, as i AM passionate about architecture
@MrFlynnIB
3 жыл бұрын
The Temple of Heaven looks like a very good one. Why can't you use it? It has to be a solid of revolution if you want to use this process. The Burj Khalifa is not one so wouldn't really work. The new Dubai Creek Tower (which will be the tallest in the world) would work. Otherwise I'm sure there are plenty more out there which would work well.
How do you test for goodness of fit?
I was told by my teacher that I could not simply state that I got my equation by using geogebra and had to explain an understanding of how they got the equation. Do you know of how I could do that? I initially used matrices for polynomial regression, but would it be wise to use a form of regression? Is there an easier way of doing it? And another issue is would it be weak to use a method that requires substituting in points, because as my teacher puts it "how do you know that the points are accurate". Which is really why I am confused on how to demonstrate my understanding of math.
@technodream9915
Жыл бұрын
my tteacher said to post a screenshot of geogebra exporting the function
Hello sir, do you know if the fitpoly function in geogebra uses the Larange extrapolation method?
@MrFlynnIB
2 жыл бұрын
Sorry I'm not sure what method is used. Let me know if you find out.
Hi Mr.Flynn, Which type of geogebra do you use? The version I am using doesn't have the button to add a 3d calculator.
@MrFlynnIB
2 жыл бұрын
The online version. Just go to geogebra.org and it's there.
Hi Mr. Flynn, thank you so much for the guidance!! i was wondering if i could do my ia on a cartoon character. I am MAA HL student. I was thinking of finding out the volume and surface area of revolution for totoro a character from studio ghibli. My reason is to make a cake with the shape. So my aim is to find out how much icing needed to coat the cake and the volume of the cake. Would this topic make a good IA? I am hoping to score my maths ia since i don’t have much confidence for the exam paper.
@MrFlynnIB
Жыл бұрын
Sounds good provided he is the right shape. Can you model him using a solid of revolution?
Hey, I'm thinking about themes for my AI in AA SL. I was thinking about finding the volume of a gummy in its normal state and after being submerged in water for some time (I saw that some gummys have this property and I want to demonstrate it using this method) i should look for the gummy shape in which it is possible to work with this theme, do you think it is a good idea?
@MrFlynnIB
Жыл бұрын
Sounds good but you are correct, you will need to find the right shape. It won't work for a normal gummy bear.
Hi!Sir. This is incredible! I'm using this method on my IA now, but i don't know how can i transfer my function into 3d culculator, the geogebra tha i found didn't have tools on the top line, instead, most of them is in a bottom called "Tools".
@MrFlynnIB
Жыл бұрын
Try this link www.geogebra.org/classic#3d
so helpful,, thanks but after that, how exactly do i calculate the volume?
@MrFlynnIB
Жыл бұрын
There is a formula in the formula booklet. Use that. All you have to do is sub in your function.
Thanks this is so helpful! One question: do you think it is a good idea to model the barbie ideal body and an average body, the calculate the volume of revolution of both and convert the units to mass and compare them? My personal engagement would be related to beauty standards, still I do not know if it is possible with this topic. Do you have any feedback please?
@MrFlynnIB
3 жыл бұрын
I don't think this works. A solid of revolution has particular properties. It is formed by rotating a curve around an axis. I don't think a barbie doll could be modelled well using this. Sorry. A good idea for you maybe (beauty and volume) might be to find the volume of a 'beauty blender' sponge. Apparently the volume doubles when it gets wet so you could test if this is true.
@BobBrown.
3 жыл бұрын
Is this a joke?
@fernandallanosm
3 жыл бұрын
@@MrFlynnIB Or maybe can I apply it using integrals? and measure the area?
@MrFlynnIB
3 жыл бұрын
@@fernandallanosm Yes this IA would work better in 2d. You could model the shape of the barbie using functions. You probably know what to do better than me after this. Maybe look if this shape is even healthy for a human.
@Oskir51
11 ай бұрын
@@MrFlynnIB Hi MrFlynn, I really like the idea about the beauty blender, and I want to explore this in my IA, I would like to know if I should go ahead with it, and if so, what advice would you give me in my process? D you think this could earn me a 7 as an sl math ai student?
how do you draw a line through the points of a topaç? it is a irregular line
@MrFlynnIB
2 жыл бұрын
Sorry I don't understand this question.
hi! great video! i was planning on doing my aa maths sl ia on something around redesigning (as product design is my interest) and so i wanted to include this concept. how could i create a good topic around this?
@MrFlynnIB
Жыл бұрын
What do you want to design?
@ST-eg2lr
Жыл бұрын
@@MrFlynnIB I looked at several options such as a watering can or a bottle but I could not think of any particular purpose for the redesign or an aim for the investigation (optimizing the surface area so that the costs/ environmental impact can be minimized has already been done a lot of times so I wanted something unique)
Thank you so much! I finally have great visuals for Math IA. However, I don't understand that after creating the shape, how do I find the volume? Is function "g" shows the equation of the curve, or am I supposed to deduce the equation using some other way? Thank you again.
@MrFlynnIB
3 жыл бұрын
You will need to use the volume of revolution formula. It's in the formula booklet.
@nayelnayel865
Жыл бұрын
@@MrFlynnIB Hello, Can I keep the height as a constant and find the radius of the bottom and radius of top of the object and use integration to find the volume?
@MrFlynnIB
Жыл бұрын
@@nayelnayel865 Isn't this the same as what I did?
Hello Sir! When I type in fit Sin it shows error, but other fitpoly and fitline works. Did I type in something wrong?
@MrFlynnIB
2 жыл бұрын
Sometimes it won't fit a particular function because of where the points are. Geogebra can sometimes be a bit finicky/annoying. Try moving the points and try again.
Great video and so helpful! However, I don't understand what is this "n" that you adjust the value of, so I can't explain it on my IA. May you briefly explain so that I understand?
@MrFlynnIB
3 жыл бұрын
It's just a quick way of changing the degree of the polynomial function. So if n=2, it is a quadratic, if n=3, it is a cubic etc. Let me know if that doesn't make sense. You don't have to use it, just put a number instead of n.
@eb5141
3 жыл бұрын
@@MrFlynnIB Oh I understand! Thank you. Just another quick question, how did you decide the size of the picture? I guess you based it on it's real life measurement if I got it correctly. Thank you again.
@MrFlynnIB
3 жыл бұрын
@@eb5141 Yes, real life measurement.
Hi! I trying to find a topic for my HL AA maths Internal assessment, would this work? do you have any ideas for my topics?
@MrFlynnIB
Жыл бұрын
Yes this would work. Check out my IA guide. Lots of ideas in there.
I really do not understand how the n works using the goodness of fit. How do I explain why I chose a polynomial to the power of 3 versus the power of 4 other than it matches the points to a better extent and I only know that based on the photo? How do i explain the goodness of fit?
@MrFlynnIB
2 жыл бұрын
This is a good and not an easy question. One thing you should calculate is the R squared value. Geogebra can also do this. The closer to 1, then the better the fit. However, you have to be careful as higher degree polynomials will always fit better than lower degree ones. But it doesn't mean that this is the best model. For example, check out my basketball shot video. A cubic or quintic model would actually have fit the data better but a quadratic is obviously the better model for a basketball shot. As a fairly general rule, with polynomials, you want the least degree that still fits the points well. Hope that helps. Just make sure that you justify your model and explain why you chose it. This will help with reflection and understanding.
@arnikumar5407
2 жыл бұрын
@@MrFlynnIB That makes sense. Another question I had when doing it was would I have to explain what polynomial regression is because geogebra created the line? Because polynomial regression is quite confusing or could I just state geogebra calculated the fit and which degree was the best?
@MrFlynnIB
2 жыл бұрын
@@arnikumar5407 You don't need to sow the polynomial regression. Yes, that gets really complicated. What you have to do which is important is justify why you chose that model and talk about goodness of fit.
Hi Mr. Flynn can you please tell me how to calculate the volume for this
@MrFlynnIB
Жыл бұрын
There is a formula in the formula booklet.
shouldnt the function be a cubic since it is 0x^4 or perhaps there is something i dont know?
@MrFlynnIB
2 жыл бұрын
Geogebra is only showing 0x^4 but really it 0.something which you can't see but which is important. If you change the number of decimal places, then you can see the extra numbers. I show how to do this in my bitcoin video.
@heykiem1908
2 жыл бұрын
@@MrFlynnIB thank u very much. ill look up your bitcoin right away
Hi, I am doing the volume of revolution for my math IA and I just found out that it has been removed from the AA SL syllabus for M'22. I'm really worried about this. Am I allowed to do something that has been removed from the syllabus?
@MrFlynnIB
2 жыл бұрын
Yes for sure. That isn't a problem but make sure you explain what you doing well enough that an SL student in your class can understand it.
@athmihasaravanen2320
2 жыл бұрын
@@MrFlynnIB Thank you so much!
I was thinking of modelling a gatorade bottle, a prime bottle. Would this topic be good? I want something with a lot of functions, I am basically in love with this topic but I don't know a good object I could do iton
@MrFlynnIB
Жыл бұрын
I think you could find better. I think even the regular gatorade bottle would be more suitable.
@technodream9915
Жыл бұрын
@@MrFlynnIB Thank you for replying, sir. Yes I agree that a gatorade bottle would be a better suitor but however, whenever I think of an object that has the rules of the solids of revolution, I can only think of bottles, and vases. So the gatorade bottle (twist top one), for me has more than 5 functions I could model it on. I want to be an industrial designer so I will relate it to how companies are able to model a bottle with abstract functions, but able to have a consistent volume within their bottle. Would this aim and object still be good? If not can you recommend any other objects I could do it on
@technodream9915
Жыл бұрын
@@MrFlynnIB Also since I am in SL, would I need to derive the formula for Solids of revolution? Since its not in the syllabus, however it is in my textbook
Hello, Sir. I got a idea now about what to do for my Math IA, but I just simply have one question to ask. In the case that, for example, the vase is abnormal such that it has different simple curves (polynomial, trigonometric...) jointed as one. Can I first express them as piecewise functions and then add them up using riemann sum? Afterwards to calculate the predicted volume, of course. And if I want to calculate the volume of the material used, can I suppose that the thickness is consistent throughout the vase? (For example, a thickness of 0,5cm on the vase I want to calculate) Thanks sir and have a nice day
@MrFlynnIB
2 жыл бұрын
Yes to both. Sounds good.
Hi! I was wondering how to find the equation for the curve. The one geogebra shows on the graph and the one it shows in the functions section aren't the same. It seems to be displaying something different than it is saying it displays. The thing it displays is correct, but geogebra doesn't correctly tell us the equation needed to graph that function.
@MrFlynnIB
2 ай бұрын
Sounds like a rounding issue. Change the number of significant figures displayed in geogebra.
@jasperdavis4840
2 ай бұрын
@@MrFlynnIB that seems to have fixed it, thanks so much.
Hi Mr Flynn, so after this video I travelled around my house for an object I could use and the best thing I could come up with is a soap dispenser. I first wonder if it's viable for an IA and if I should calculate volume or surface of revolution?
@MrFlynnIB
Жыл бұрын
You could do either. Or both. Depends what you want the aim of your IA to be. Try to find a reason for getting the volume or surface area.
@thisismurica6310
Жыл бұрын
@@MrFlynnIB Could I say I want to use the volume to know to know the quantity of soap that can be put in? Thanks for the reply
@MrFlynnIB
Жыл бұрын
Ya I guess that works.
did you revolve around the x-axis for y-axis
@MrFlynnIB
Жыл бұрын
This example is revolved around the x axis but you can revolve around the y axis too.
Do I have to find equation for both sides of the picture?
@MrFlynnIB
2 жыл бұрын
No, just one. Then rotate it 360 degrees around the x-axis.
How do i can find the volume of the surface generated into the geogebra?
@MrFlynnIB
11 күн бұрын
You need to use the formula for the volume of a revolution. It is in the HL formula booklet.
would it be possible to optimize the volume or SA of a curved shape?
@MrFlynnIB
Жыл бұрын
Yes.
@allysona843
Жыл бұрын
@@MrFlynnIB I mean, for an object that is for instance like a round teddy bear. Also would it be too difficult to find the minimum surface area of revolution? and how would one go about it.
@MrFlynnIB
Жыл бұрын
@@allysona843 You could find the surface area of revolution. There is a formula. To find the minimum surface area is different. What does minimum surface area mean in this case? Are you going to change the shape of the bear?
Great video! I am in AA HL and struggling to find a good topic that would allow me to use the HL math concepts, how could I build a good topic that uses this concept?
@MrFlynnIB
2 жыл бұрын
You need to find an object that is a solid of revolution for which you want to find the volume. A good example that I have seen (maybe I mentioned it in the video) was a beauty blender sponge. Apparently the volume of this sponge doubles when it is wet. One of my students wanted to find out if this was true so she used this topic.
@karimkhaddour4720
2 жыл бұрын
@@MrFlynnIB Would measuring the volume versus the surface area of the bottles of sprite and Coca-Cola to see which optimizes the use of plastic be a good topic for AA HL?
@MrFlynnIB
2 жыл бұрын
@@karimkhaddour4720 Ya not bad but really you know the volume as it says it on the label (unless you aim to verify this) so really it would be more about finding the surface area to see which is smaller. Which works fine.
@sunniva7786
Жыл бұрын
@@MrFlynnIB Do you think i could use this as well and if so what would the rq be does the volume of a beauty blender double when getting wet?
@MrFlynnIB
Жыл бұрын
@@sunniva7786 Remember it is an aim, not a research question. But ya, that sounds like a good aim.
Hi which geogerbra is this because mine dont have the button to both 2d and 3d like you did in this vid?
@arianaazmir4321
9 ай бұрын
Nevermind found it already, anyone else who face the same trouble as mine, try using geogebra classic 6.
@sayuritrinidadgallinarvazq1996
8 ай бұрын
@@arianaazmir4321 where do u find geogebra classic 6?
wow
Sir may I learn which program do you use in this video ?
@MrFlynnIB
2 жыл бұрын
geogebra.org it's online and free.
is there any way for me to find the surface area of revolution from this volume of revolution graph?
@MrFlynnIB
Жыл бұрын
Yes. There is also a formula for surface area of a revolution. It is not in the formula booklet but easily found online.
@StrawberryS-vk5my
Жыл бұрын
@@MrFlynnIB i see but can i use this f(x) equation for the surface area of revolution as well
@MrFlynnIB
Жыл бұрын
@@StrawberryS-vk5my yes.
hey, im doing the Math Sl and i need to finish my IA within a week. is this a good topic to do my IA on
@MrFlynnIB
2 жыл бұрын
Ya but find something interesting to get the volume on. And a week is not a lot of time. Let me know how you get on.
@gokupods4088
2 жыл бұрын
@@MrFlynnIB thinking of doing the volume of funko pop
@MrFlynnIB
2 жыл бұрын
@@gokupods4088 It's not really a solid of revolution so won't work well.
Thank you for this video sir. Would it be a good topic for a Math AA HL student aiming for a 7?
@mateogullon3092
3 жыл бұрын
Do you recommend volumes of revolution or modelling (bitcoin, for example)?
@MrFlynnIB
3 жыл бұрын
Yes it is a good topic. Volume of revolution is not in the SL course so good for HL.
@MrFlynnIB
3 жыл бұрын
Both are good ideas. I would choose the one that interests you more.
@mateogullon3092
3 жыл бұрын
@@MrFlynnIB Thank you sir. I was thinking of modellating the sea level rise along time. Since I am in AA HL, would it be a good idea to get the line of tendency manually instead of using Excell/Geogebra (with the proofs of the statements I use, which some of them include calculus)?
@MrFlynnIB
3 жыл бұрын
@@mateogullon3092 What kind of model are you think of using? Linear? I could work but generally I don't recommend this for HL.
Hi Mr. Flynn! I have a question: at 3:00, why did you leave out the small bit on the left rather than move it all to the right of the y-axis?
@MrFlynnIB
Жыл бұрын
No good reason. I probably shouldn't have.
@kellyjin2469
Жыл бұрын
@@MrFlynnIB Ok! Also, would this be enough for an HL IA? The IA has to be 12-20 pages I believe and I'm not sure if I will have enough to fill up that many pages :(
@MrFlynnIB
Жыл бұрын
@@kellyjin2469 I have seen many IAs on this topic in the 12-20 page range. Some done well. Some done not well.
@kellyjin2469
Жыл бұрын
@@MrFlynnIB Thank you! Also, the best fit function shows up on GeoGebra correct?
@MrFlynnIB
Жыл бұрын
@@kellyjin2469 you have to tell Geogebra which function to try and fit and then Geogebra will find the function of that type that best fits the points you give it.
5:44, How do u find goodness of fit?
@MrFlynnIB
4 ай бұрын
I meant talk about how well the function fits the curve. The R squared value is one measure but be sure not to solely rely on this.
The graph that Geogebra gives me, is completely wrong. Whemever I type the function for L1 into a graphing calculator, the graph comes out to be completely different.
@MrFlynnIB
Жыл бұрын
I'm confident this is a significant figures issue. Increase the number of significant figures in settings.
Can I take any picture of vase from Internet for my IA?
@MrFlynnIB
2 жыл бұрын
Try to think of a good reason why you want to find the volume. Does it have to be a vase? I would take my own photo if possible.
Hello sir, your videos are brilliant! I really love them!! I'm currently doing an IA HL where I'm interested in finding out the surface area of revolution where Geogebra has come up with a 6th degree polynomial. Can you please guide me how to go about working out Surface Area using ∫2πf(x) √(1+(f^' (x))^2 ) dx〗that involves square root of a function having a square of a 6th degree polynomial. Is there any math tool available to compute this? Many thanks
@MrFlynnIB
2 жыл бұрын
Thanks. Glad they are useful. A decent online calculator should be able to do what you need. Try desmos.com.
Thank you so much for this, this is amazing! Sir I was just wondering if you are interested to do some IA guidance videos in modeling COVID 19 using SIR, it would be truly appreciated
@MrFlynnIB
3 жыл бұрын
Thanks Jenny. I'm not a huge fan of the SIR model for an IA. But this is probably because I have not seen many good ones. It is difficult. I'll have a think and maybe make a video.
@jennyzhang2810
3 жыл бұрын
@@MrFlynnIB Thank you so much for considering it! It will be extremely helpful:)
Mr Flynn why do you sound so down? Also could I use this the determine the volume of a plastic bottle like a coca cola?
@MrFlynnIB
3 жыл бұрын
Haha not sure. Maybe I was having a bad day. Ya absolutely for the coke bottle.
@marcusb.7412
3 жыл бұрын
@@MrFlynnIB any idea how I would determine the surface area of the coke bottle? I was thinking about doing an optimization IA (volume o surface area) for HL
@MrFlynnIB
3 жыл бұрын
@@marcusb.7412 There is a surface of revolution formula that you can use. It is not in the syllabus but works well.
can I do this for SL IA?
@MrFlynnIB
Жыл бұрын
Yes. Note: it is not in the syllabus so you will need to explain it as if the reader has never heard of it.
@nasirahmad7792
Жыл бұрын
@@MrFlynnIB hi sir, how would one approach it? Do we just explain the concept or also the math like in the textbook?
@MrFlynnIB
Жыл бұрын
@@nasirahmad7792 Watch my 8 part IA guide. This will give you a good idea of what is expected.
Hello Mr Flynn, Just asking for some advice on my idea for my Maths AA SL IA. I was thinking of optimising the shape of a moisturiser face cream container to hold the most cream, taking inspiration from this video: kzread.info/dash/bejne/dJ18yrV6pJS0gLQ.html I think it may be possible, but I am a bit uncertain with the specifics involved and if I were to go ahead and complete calculations such as, a volume of revolution, during the process - would this maths be too advanced for the average AA SL student? I really appreciate all your videos and time.
@MrFlynnIB
27 күн бұрын
Hey. I think this is a good idea. Just keep it simple. Don't overcomplicate it and the maths should be fine for an SL student.
Hi sir, the online version does not have the 3D calculator version. Is there an alternative application that I can use?
@MrFlynnIB
Жыл бұрын
It does.